By 91 percent to 8 percent, voters also approved of stricter penalties both for people who illegally buy guns and for those who use guns on school grounds.

On Tuesday, Cuomo signed a new law that addresses those and other issues in a comprehensive gun-control bill. New York became the first state in the nation to tighten its gun laws in the wake of the Newtown, Conn., school massacre on Dec. 14.

"While this poll was conducted prior, during and after Cuomo's gun proposal was made public and enacted, New Yorkers -- who view the National Rifle Association unfavorably by a 57 percent to 36 percent margin -- overwhelmingly support the ban on assault weapons and nearly unanimously support increasing penalties for purchasing illegal guns and using guns on school grounds," Siena College pollster Steven Greenberg said.

Siena surveyed 676 voters across New York on Jan. 10 and from Jan. 13-15. The poll has a margin of error of plus or minus 3.8 percentage points.